Question: Simplify the following expression: $ t = \dfrac{7}{10} + \dfrac{10r}{-r + 3} $
Solution: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{-r + 3}{-r + 3}$ $ \dfrac{7}{10} \times \dfrac{-r + 3}{-r + 3} = \dfrac{-7r + 21}{-10r + 30} $ Multiply the second expression by $\dfrac{10}{10}$ $ \dfrac{10r}{-r + 3} \times \dfrac{10}{10} = \dfrac{100r}{-10r + 30} $ Therefore $ t = \dfrac{-7r + 21}{-10r + 30} + \dfrac{100r}{-10r + 30} $ Now the expressions have the same denominator we can simply add the numerators: $t = \dfrac{-7r + 21 + 100r}{-10r + 30} $ $t = \dfrac{93r + 21}{-10r + 30}$ Simplify the expression by dividing the numerator and denominator by -1: $t = \dfrac{-93r - 21}{10r - 30}$